Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#1271 ⋊ C2 |
| Sylow | C7 ⋊ #7747 |
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|b^2=fgh,c^2=f,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,i^a=i^6,d^b=df,e^b=eg,i^b=i^6,d^c=dg,e^c=eh,i^c=i^6151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 58342);